The values of a for which \left(\right. 8 , - 7 , a \left.\right) , \left(\right. 5 , 2 , 4 \left.\right) and \left(\right. 6 , - 1 , 2 \left.\right) are collinear, is given by?

Engineering

Mathematics

Line of Greatest Slope

Question

The values of a for which

(8, - 7, a), (5, 2, 4)

and

(6, - 1, 2)

are collinear, is given by?

2

- 2

- 1

1

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\begin{array}{c} t h e n a = ? \\ T h e e q u a t i o n l i n e A B i s, \\ \Rightarrow \frac{x - 8}{5 - 8} = \frac{y + 7}{2 + 7} = \frac{z - a}{4 - a} . . . . (1), \\ p o i n t c l i e s i n t h e l i n e A B \\ p o i n t (6, - 1, 2) s a t i s f y e q (1), \\ \Rightarrow \frac{- 2}{- 3} = \frac{- 1 + 7}{9} = \frac{2 - a}{4 - a}, \\ \Rightarrow \frac{2}{3} = \frac{2 - a}{4 - a}, \\ \Rightarrow 8 - 2 a = 6 - 3 a \\ \Rightarrow 3 a - 2 a = 6 - 8 \\ a = - 2 \\ , \end{array}

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